Let us begin with some terminology. Mathematics is not arithmetic. Arithmetic is a tool used with Mathematics, but Math doesn’t actually begin until Algebra. Before that, it is arithmetic, which is our Four Basic Operations … adding, subtracting, multiplying, and dividing … with whole numbers, fractions, decimals, and percents. Arithmetic also includes measurements … length, weight, time, money, etc.
Adding and Subtracting. These are flip sides of the same coin. One will undo the other, so it is great to learn them together. 2+2=4 and 4-2+2 can be learned at the same time. I found with the youngest ones to use the terms “and” and “take away” or “less” instead of “plus” and “minus” made far more sense to them. Also, saying “are” instead of “equals” or “is” is also grammatically correct. Two and two are four; four take away two are two. At first, it seems awkward, but it will begin to feel natural to you quite soon.
This is also a great place for the dreaded “rote memorization.” Spending a few minutes each day reciting some arithmetic facts will actually help the children learn them faster and better. For this, I took my cue from “Ray’s Arithmetics” published by Mott Media. The top of a page will have all the “twos” written out. I would say a line, the child would repeat it. For instance, two and three are five; three and two are five; two and four are six; four and two are six. We did this over and over. It did not allow for making any mistakes, so the correct facts were learned. They “heard it” and they “said it.” Double the effectiveness. Incidentally, that only takes a few minutes each day, but it works.
Concentrating for just ten minutes, and everything said is correctly, will result in better retention than dreading the half hour or hour of traditional arithmetic time, where there is too much busy work and mistakes are common. Once you get the hang of doing it this way, you will be amazed.